Optimization design for TPMS lattice structures combining density gradient with hybridization
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Abstract:
The triply periodic minimal surface (TPMS) lattice structures have attracted extensive attention from scholars worldwide. In practical applications, these lattice structures are typically designed optimally to meet the requirements of both lightweight and load-bearing capacity. However, current optimal designs for TPMS lattice structures are limited to density gradients, and the influence of loading directions on their mechanical properties has not been comprehensively considered. To address this gap, the anisotropic characteristics of TPMS lattice structures were investigated. Their equivalent elastic matrixes were calculated by using the homogenization method, and three-dimensional Young’s modulus diagrams were generated with Matlab. The results showed distinct anisotropy characteristics for different types of TPMS lattice structures. For instance, the W structure exhibited higher strength in the axial direction [100] and weaker strength in the diagonal direction [111]; whereas the P structure showed the opposite trend. Subsequently, an optimization design method was proposed, combining density gradient with hybridization, considering both density distribution and principal stress directions. The optimization process involved topology optimization of a cantilever beam structure, and mapping the obtained density cloud to the relative density distribution of the lattice structure. Based on the anisotropic characteristics of TPMS lattice structures, W and P lattice cells were selected to fill the cantilever beam, aligning the principal stress directions with the strong mechanical properties of the lattice cells. After reasonable distribution of TPMS lattice cells of different types, they were smoothly connected by an activation function. Finally, the relative density and lattice cell type distributions were combined to obtain a density-graded hybrid lattice structure. The load-bearing performances of lattice structures before and after optimization designs were compared through finite element analysis. The results showed that the stiffness of density gradient W and P lattice structures was significantly improved compared with uniform structures. Moreover, the stiffness of the graded hybrid lattice structure was the highest, surpassing the density gradient W and P lattice structures by 4.63% and 33.63%, respectively. This demonstrates that hybridization design, achieved through a reasonable distribution of different lattice cells according to principal stress directions, can further improve overall stiffness. The established optimization method, combining density gradient with hybridization for TPMS lattice structures, provides a guidance for their application in lightweight designs.
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Supported by the Key Project of the Natural Science Foundation of Chongqing (cstc2020jcyj-zdxmX0021).
